The recovery of three-dimensional configurations of a scence from its image is one of the most important steps in computer vision. The Origami world is a model for understanding line drawings in terms of surfaces, and for finding their 3-D configurations. It assumes that surfaces themselves can be stand-alone objects, unlike the conventional trihedral world which assumes solid objects. we have established a labeling procedure for this Origami world, which can find the 3-D meaning of a given line drawing by assigning one of the labels, + (convex edge), – (concave edge), ←, and → (occluding boundary) to each line. The procedure uses a filtering procedure not only for junction labels as in the Waltz labeling for the trihedral world, but also for checking the consistency of surface orientations. The theory includes the Huffman-Clowes labelings for the trihedral solid-object world as a subset. This paper also reveals interesting relationships among previous research in polyhedral scene analysis.